Torsional Wave in a Dissipative Cylindrical Shell Under Initial Stresses

The dispersion relation of torsional wave in a dissipative,incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated.The governing equation and closed form solutions are derived with the aid of Biot’s principle.Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details.We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form.Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs.The analytical and numerical solutions reveal that,the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell.The numerical results reveal that,the initial stresses and dissipation,considerably,effect the phase velocity of the torsional wave.It has been observed that,any change in dissipation parameter(δ)produces a substantial change in damping velocity of torsional wave.In addition,it can be seen that,the phase velocity increases as the initial stress parameter increases.Finally,the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation.The conclusion made shown the consistency with the Biot’s incremental deformation theory,and the effective on model such as engineering mechanics and displacement of particles.

Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer

The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types, namely, exponential, quadratic, and hyperbolic discussed separately. The dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equa- tion of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.

Torsional wave in a circular micro-tube with clogging attached to the inner surface

In the present paper, we study the torsional wave propagation along a micro-tube with clog- ging attached to its inner surface. The clogging accumulated on the inner surface of the tube is modeled as an ＂elastic membrane＂ which is described by the so-called surface elasticity. A power-series solution is particularly developed for the lowest order of wave propagation. The dispersion diagram of the lowest-order wave is numerically presented with the surface （clogging） effect.

Effect of rigid boundary on propagation of torsional surface waves inporous elastic layer

The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato （Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13（2）, 125-147 （1983））. The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. （Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6（4）, 241-249 （2003））. The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.

Effect of irregularity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer

The paper studies the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity is taken in the half space in the form of a rectangle. It is observed that torsional surface waves propagate in this assumed medium. In the absence of the irregularity, the velocity equation of the torsional surface wave is also obtained. For a layer over a homogeneous half space, the velocity of torsional surface waves coincides with that of the Love waves.

An analytical approach to reconstruction of axisymmetric defects in pipelines using T(0,1)guided waves

Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),which is the first order of torsional guided waves,plays the irreplaceable position and role,mainly because of its non-dispersion characteristic property.However,one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy.Taking into account this situation,a quantitative reconstruction method using the torsional guided wave T(0,1)is proposed in this paper.The methodology for defect reconstruction consists of three steps.First,the reflection coefficients of the guided wave T(0,1)scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method(HFEM).Then,applying the boundary integral equation(BIE)and Born approximation,the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T(0,1)and the fundamental solution of the intact pipeline in the frequency domain.Finally,reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain.Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile,the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated.It is noted that the reconstructive error is less than 10%,providing that the defect depth is no more than one half of the pipe thickness.

DETECTION OF LONGITUDINAL DEFECT IN PIPES USING TORSIONAL MODES

The multi-modes and disperse characteristics of torsional modes in pipes are investigated theoretically and experimentally. At all frequencies, both phase velocity and group velocity of the lowest torsional mode T（0,1） are constant and equal to shear wave velocity. T（0,1） mode at all frequencies is the fastest torsional mode. In the experiments, T（0,1） mode is excited and received in pipes using 9 thickness shear vibration mode piezoelectric ceramic elements. Furthermore, an artificial longitudinal defect of a 4 m long pipe is detected using T（0,1） mode at 50 kHz. Experimental results show that it is feasible for longitudinal defect detection in pipes using T（0,1） mode of ultrasonic guided waves.